Proving $7 + 7^2 + 7^3 + \cdots + 7^n = \frac{7^{n + 1} - 7}{6}$ using Induction

Question

Currently, I'm trying to prove an equation by induction and here's what i have done so far. I've attached my working i've done in jpg format below.

Answer 1

The last step is not right.

the left hand side works out to:

$$\frac{7^{k+1}-7+6*7^{k+1}}{6}= \frac{1*7^{k+1}+6*7^{k+1}-7}{6}=\frac{7*7^{k+1}-7}{6}=\frac{7^{k+2}-7}{6}$$